The obvious and simple answer to the above question is God, but there is more to it than that. First of all, many men question the authority of God to judge people, not only in eternity, but here in this life. They arrogantly challenge Him and declare that either He does not exist at all, or that He does not have the power to bring them into judgment. Some people do this overtly, and some do it by their actions. "Why do the heathen rage, and the people imagine a vain thing? The kings of the earth set themselves, and the rulers take counsel together, against the LORD, and against his anointed, saying, Let us break their bands asunder, and cast away their cords from us. He that sitteth in the heavens shall laugh: the Lord shall have them in derision. Then shall he speak unto them in his wrath, and vex them in his sore displeasure (Ps 2:1-5)." The disciples quoted this passage when they prayed after being threatened for their testimony (Acts 4). Whenever someone dares to say that some event was a judgment of God, there is huge backlash and demands for apology for their insensitivity. While the role of the church is to offer compassion, the underlying message is that God cannot do such things. I don't know what Bible they are reading because God does this all the time on the small and large scale.
When speaking about the authority of God over man and man's foolish questioning of it, Paul said, "Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus (Rom 9:20)?" The holiness of God and His justice demand judgment for evil. That is why He came in the flesh and died for us (Jn 1:1-3 & 14, Jn 3:16, Jn 10:30, Jn 14:7-11, 2Cor 5:19, Col 2:8-12, 1Tim 3:16). He took His own judgment upon Himself so we could escape. Yet this does us no good unless we apply what He did for us according to His word (Acts 2:37-39). He does not desire to judge us (Eze 18:32, Eze 33:11), but if we do not repent and obey the gospel, we leave Him with no choice even after all He has done for us (Rom 14:10, 2Cor 5:10, Rev 20:11-15). We complain when someone seems to get away with evil, bu then we accuse God of injustice if He judges someone. We can't have it both ways.
His ways are far above our ways, and we are in no position to question His decisions (Eze 18, Is 55:6-9). We must also remember that God is merciful beyond our understanding. When He does judge, it is only after many attempts to turn people from their path.
Herein lies the problem. It is not so much God, judging us as it is us receiving the inevitable consequences of our actions. There are unavoidable laws of nature. If we step out in front of a truck on the highway, we will be given immediate evidence of this. The same is true spiritually. We can no more avoid it than we can the results of the impact of the truck on our 150 pound body. We reap what we sow, whether good or evil. "Be not deceived; God is not mocked: for whatsoever a man soweth, that shall he also reap. For he that soweth to his flesh shall of the flesh reap corruption; but he that soweth to the Spirit shall of the Spirit reap life everlasting (Gal 6:7-8)." People call this karma after the Koran, but the Bible said this 600 years earlier.
Even those who are not familiar with the Bible are given a more than fair chance. "For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse (Rom 1:20)." The creation shows us a God of infinite power. It shows He is the origin of life, matter, energy, and information. It shows His love and beauty. It shows there is only one God. The law and order of creation reflects His nature. Dating methods, genetics, natural selection, irreducible complexity, mathematical odds, laws of nature vs. randomness, the fossil record, no other explanation for the origin of life and matter and information and energy, the circular reasoning of evolution, Mt. St. Helens, and even Darwin’s own admissions show the fallacy of denying our Creator. However, the evolutionists fulfill Rom 1:18-32 by denying the truth of the Creator so they can ignore accountability to Him. They also have their own conscience as a witness (Rom 2:1-15). When someone seeks God and His truth, He makes sure they have the opportunity to find it. When they openly reject Him, He lets them make their choice. So then they are really judging themselves. Paul always tried to reach his people the Jews, for whom he had a great burden (Rom 9:1-5). He always went to them first with the gospel in his travels. He would start his campaign in a city by going to the synagogue if there was one. Yet when they openly rejected their opportunity, he told them, "It was necessary that the word of God should first have been spoken to you: but seeing ye put it from you, and judge yourselves unworthy of everlasting life, lo, we turn to the Gentiles (Acts 13:46)." God gave them their opportunity, but they rejected it and will be judged by their own actions.
There are 3 criteria mentioned in Revelation 20:11-15, which describes the great final judgment of humanity. There are the book of life which is the record of all who have chosen to be saved, the Bible, and the record of everyone's deeds and whether or not they lived by the word of God. So it is really us who are the judges. Every day we make decisions which will affect us now and in eternity. So it is really us who are the judges of our own selves. God merely makes sure the principles of His word are indeed in effect. Whether that works for our salvation or destruction is up to us. God already decided He wants to save us. The question is not on Him. It is on us. "For if we would judge ourselves, we should not be judged (1Cor 11:31)."